Quantum resource theory of coding for error correction
arXiv:2409.09416 · doi:10.1103/PhysRevA.110.032413
Abstract
Error-correction codes are central for fault-tolerant information processing. Here we develop a rigorous framework to describe various coding models based on quantum resource theory of superchannels. We find, by treating codings as superchannels, a hierarchy of coding models can be established, including the entanglement assisted or unassisted settings, and their local versions. We show that these coding models can be used to classify error-correction codes and accommodate different computation and communication settings depending on the data type, side channels, and pre-/postprocessing. We believe the coding hierarchy could also inspire new coding models and error-correction methods.
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